Predicting NBA All-Star Chance Based on Player Performance
By: Bill Makwae, Ayush Vora, Ray Nguyen, QingRu Kong
Modified by: Ray Nguyen, Jeffrey Song, Emilio Dorador, Berkay Talha Acar
1 Introduction
Every year in February, NBA fans rejoice as they get to see their favorite players selected for the all-star game. Players are selected by media and fan votes, meaning that popularity is the dominating factor. However, players are more likely to be popular based on their individual game-to-game performance (Grimshaw and Larson (2021)). Thus, this analysis hopes to answer the question: Can an NBA player’s selection to the all-star game be predicted by their annual performance?
In order to answer this question, we will be using two sets of data, one from “NBA Player Stats” on nba.com and “NBA All Stars 2000-2016” from kaggle.com. NBA Player Stats includes all the NBA player statistics for each season from 2010-2016 and the All Star dataset includes the all star statistics from 2000-2016. Using these datasets we aim to make a classification model that will predict whether a player will be an all star for each season based on their annual performances.
The variables that we will be looking at for this data set are the following:
- Year: Season that the player played.
- Player: Name of the player.
- MIN: Average number of minutes that the player played per game.
- PTS: Average number of points that the player scored per game.
- FG.: Field Goal Percentage.
- REB: Average number of rebounds that the player made per game.
- AST: Average number of assists that the player got per game.
- Is_All_Star: Whether the player was an All-Star in that season.
This is our classifier.
We chose these variables because they are the most indicative of a player’s offensive output, which is the main focus of the all star game (N. Nguyen, Ma, and Hu (2020))
2 Methods and Results
The dataset is generated is a combination of two datasets which filtered using a left join method specified in the function getallstars(). The final dataset only keeps allstar players specified in the year range. Below is a sample of the output.
| Year | Player | GP | MIN | PTS | FGM | FGA | FG. | X3PM | X3PA | X3P. | FTM | FTA | FT. | OREB | DREB | REB | AST | STL | BLK | TOV | Is_All_Star |
|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|
| 2011 | Kevin Durant | 78 | 38.9 | 27.7 | 9.1 | 19.7 | 46.2 | 1.9 | 5.3 | 35.0 | 7.6 | 8.7 | 88.0 | 0.7 | 6.1 | 6.8 | 2.7 | 1.1 | 1.0 | 2.8 | All Star |
| 2011 | LeBron James | 79 | 38.8 | 26.7 | 9.6 | 18.8 | 51.0 | 1.2 | 3.5 | 33.0 | 6.4 | 8.4 | 75.9 | 1.0 | 6.5 | 7.5 | 7.0 | 1.6 | 0.6 | 3.6 | All Star |
| 2011 | Carmelo Anthony | 77 | 35.7 | 25.6 | 8.9 | 19.5 | 45.5 | 1.2 | 3.3 | 37.8 | 6.6 | 7.9 | 83.8 | 1.5 | 5.8 | 7.3 | 2.9 | 0.9 | 0.6 | 2.7 | All Star |
| 2011 | Dwyane Wade | 76 | 37.1 | 25.5 | 9.1 | 18.2 | 50.0 | 0.8 | 2.7 | 30.6 | 6.5 | 8.6 | 75.8 | 1.6 | 4.8 | 6.4 | 4.6 | 1.5 | 1.1 | 3.1 | All Star |
| 2011 | Kobe Bryant | 82 | 33.9 | 25.3 | 9.0 | 20.0 | 45.1 | 1.4 | 4.3 | 32.3 | 5.9 | 7.1 | 82.8 | 1.0 | 4.1 | 5.1 | 4.7 | 1.2 | 0.1 | 3.0 | All Star |
| 2011 | Amar’e Stoudemire | 78 | 36.8 | 25.3 | 9.5 | 19.0 | 50.2 | 0.1 | 0.3 | 43.5 | 6.1 | 7.7 | 79.2 | 2.5 | 5.6 | 8.2 | 2.6 | 0.9 | 1.9 | 3.2 | Regular |
We used set.seed(2022) to ensure the same set of data is used and the data set is reproducible. Used initial_split() function to split the data set into 70:30 ratio of training and testing data. We choose 70:30 ratio because it is an optimal ratio to represent the training and testing data, as we want to maximize data used for training but still leave some data left for testing the classification model. Is_All_Star is assigned as the strata because it is the classifier we want to find. 70% of the data is assigned to data_training using training(), and 30% of the data is assigned to data_testing using testing().
We want to calculate the average for each variable by first group the observations by Is_All_Star and then use summarize() to compute the means.
| Is_All_Star | MIN | PTS | FGM | FGA | FTM | FTA | TOV |
|---|---|---|---|---|---|---|---|
| All Star | 35.00896 | 19.87463 | 7.217910 | 15.159702 | 4.343284 | 5.39403 | 2.511940 |
| Regular | 25.66599 | 10.41489 | 3.936496 | 8.645547 | 1.772263 | 2.34219 | 1.424088 |
We still grouped by Is_All_Star and used summarize to calculate the number of observations for each group then divided by the total number of observations.
| Is_All_Star | Counts | Percent |
|---|---|---|
| All Star | 67 | 8.909574 |
| Regular | 685 | 91.090425 |
We used ggpairs() from the GGally library to make a scatterplot for every pair of variables to visualize the relationship between them. By doing so, we can see what variables truly distinguish All Star players from regular players.
Figure 2.1: Player Distributions of Various Players Statistics
Cross validation(vfold_cv) will give us a higher accuracy as it split our training data into 4 training and 1 testing. This way, there would be 5 tests done to evaluate the accuracy of the model instead of just one. We chose to fold by 5 because our dataset is quite large, folding by 10 will take too much time for the kernel to run. We create the k-vals data frame with the “neighbors” variable containing values from 1 to 70, stepping by 5, using the seq function. After experimenting with different K ranging, 1 to 70 step by 5 run in a relatively short period of time while giving us a decent K range, therefore we chose it as our K range.
Then, we create a recipe by setting the classifier to be Is_All_Star and the rest are predictors. Next, we centered and scale the data with step_center() and step_scale(). After, we balanced the data using step_upsample(), since All-Stars only make up 10% of the dataset (as shown by proportions), now the all star and regular variable will be at a 1:1 ratio. Afterward, we created a tuning model specification for K-nearest neighbors classification by calling nearest_neighbors() and setting the engine to be “kknn” with set_engine() and the model to be “classification” with set_mode(). We chose classification because our classifier is a factor, and we are trying to find whether a player will be all star or regular player which does not involve numeric value output.
Lastly, we add the recipe and the model specification into a workflow and let it run the cross validation test on data_fold by passing k_vals into grid argument of tune_grid(). Then we use collect_metrics() and filter() to only look at the “accuracy” part of .metric to acquire the accuracy of our model for each K.
When we graphed the various possible K values by accuracy, it seemed like 1 is a good K but this is not accurate because it leads to overfitting. Instead, we chose an odd number that is near 60, such as 61. As we have experimented, any K value ranging from 30-70 does not make too much difference to the accuracy of predicting the All Star player, therefore, we chose 61 as it has the highest model accuracy rate within the 30-70 K range.
Figure 2.2: Plot of estimated accuracy versus the number of neighbors
The above graph shows the accuracy for each neighbour input. The highest accuracy is near the first K. A steep decline to 0.825 when we have one neighbour vs 15 neighbours and a gentle decline from 15-32 neighbours. Starting from ~32 neighbours the accuracy increase to a small peak every 10 neighbours and decline by half every 10 neighbours.
After we determined the best K value for our model, we updated our model by setting neighbours to 61. Then, we updated the workflow to add the recipe, the updated model, and fit the training data with fit(). We are using the testing data as this is used to test the accuracy of our model with data unseen before. Finally, we used the predict() function with our model and our testing data to see how well our model performed. Then, we bound our columns with the testing data to see the data and predictions side-by-side.
We found the accuracy of the classifier by using the metrics() function on the data_prediction dataframe. By setting the truth parameter to Is_All_Star and the estimate parameter to .pred_class, we ended up with a frame of data metrics for when our classifier tries to predict the All Star players. We then filtered the .metric column by the accuracy tag with filter() and selected the .estimate column to find the accuracy of our model with select(). The overall accuracy of our predication model is 80.7%.
Next, we used conf_mat() on the data_prediction data frame to create a confusion matrix of our classifier’s results. Which shows that our All Star prediction accuracy is 23/26(88.5%), and regular prediction accuracy is 237/296 (80.1%).
## Truth
## Prediction All Star Regular
## All Star 33 48
## Regular 2 240Above is a confusion matrix displaying how many All Star and Regular our model prediction is correct and wrong. Out of 26 All Star, our model predicted 23 All Star correctly and 3 wrong. Out of 296 Regular players, 237 players are predicted correcly and 59 were predicted wrong. This brings our accuacry of All Star to 88.5%.
We created a data frame based on the confusion matrix above using the tibble() function. Then we plotted a percent stacked bar graph with the correctness ratio on the y axis and All Star or Regular label on the x axis. This graph shows that the model is more accurate when predicting the All Star players than the Regular players, but both still have a high accuracy.
Figure 2.3: The blue shade represent the players that our model predicted correctly, while the red shaded area represent the players that our model predicted incorrectly. Overall 0.885 of all star players was predicted correctly, while 0.801 of the regular players were predicted correctly.
3 Discussion
3.1 Summarize what you found
We found that using our classifier correctly identified a player to be an all-star 88.5% of the time. This is shown by our confusion matrix where 23/26 all-stars were correctly identified. However, the classifier incorrectly classified regular players as all-stars 59/256. This reduced our overall prediction accuracy to 80.1%. As a general takeaway, the higher a player’s statistics (at least the ones we observed in this study) meant that a player was more likely to be an all-star.
3.2 Discuss whether this is what you expected to find?
This analysis went as expected. We initially thought that higher player statistics would be a good identifier of an all-star player, and our classifier showed this. Our classifier was able to improve the accuracy of identifying an all-star player by over 44.5% percent over a fifty-fifty guess model.
3.3 Discuss what impact could such findings have?
The impact of our findings could include: helping organizations determine player value when negotiating player contracts to maximize the return outcome of their investment, determining trade value, and even the overall organization value. Our model would also allow teams to focus resources on certain players in order to increase their chance of earning the all star title (Liu (2021)).
3.4 Discuss what future questions could this lead to?
Future studies could look at weighing the different player statistics differently based on their perceived value, and see if there are certain statistics that are more influential in predicting a player’s all-star status (N. H. Nguyen et al. (2022)). Another study could look at classifying whether a player is a good fit for the team, as the player could address any weaknesses in their offense or defense.